# The 8th term of an AP is zero. Prove that its 38th term is triple its 18th term.

Let a be the first term and d be the common difference.

Given: a8 = 0

To prove: a38 = 3 × a18

Now, Consider a8 = 0

a + (8 - 1)d = 0

a + 7d = 0

a = - 7d ……. (1)

Consider a38 = a + (38 - 1)d

a38 = - 7d + 37d (from equation (1))

a38 = 30d ………. (2)

Now, consider a18 = a + (18 - 1)d

a18 = - 7d + 17d (from equation (1))

a18 = 10d ……….(3)

From equation (2) and (3), we get,

a38 = 3 × a18

Hence, proved.

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